Monday, 3 February 2014

An attempt at Golden Balls in class

Today I introduced my students to the concepts of Dominance and Best responses in my new game theory class (Chapters 3 and 4 of my class notes).

To re-affirm ideas we saw previously (normal form representation of games) and also talk about Dominance I tried to set up a kind of Golden Balls game.

Golden Balls is a game show that aired in the UK a while ago and I've never actually seen an episode but the premise is that two players cooperate during the game to come up with a total sum of money that must then be 'shared' using a Prisoner's Dilemma.

If you haven't seen this video before, it's a great example of the end game of the show:



I always show this video to students when talking about Game Theory as I reckon it's pretty awesome.

Here's what I did in class:

I got two students to play the game: A and S. They were to compete against me (as the row player, I was the column player) in the following 5 normal form games (their utility corresponded to the number of chocolates I would owe them):

1. Just a plain old matching pennies game (we played this in class last week and I blogged about it here):

$$\begin{pmatrix}
(1,-1)&(-1,1)\\
(-1,1)&(1,1)
\end{pmatrix}$$

2. A modification of this game with a weakly dominated strategy:

$$\begin{pmatrix}
(1,-1)&(-1,1)\\
(1,-1)&(1,-1)
\end{pmatrix}$$

A and S were both quick to realise  that they should play the second row strategy.

3. A modification of the matching pennies game:

$$\begin{pmatrix}
(2,-2)&(-1,1)\\
(-1,1)&(2,-2)
\end{pmatrix}$$

4. A game with a strategy at which they would definitely win something:

$$\begin{pmatrix}
(2,-2)&(1,-1)\\
(-1,1)&(2,-2)
\end{pmatrix}$$


5. The same game as 4, again (when I play this next year I'll change this game slightly).

This ended up with A and S having about 6 chocolates between them. I then split the team up and told them to play:

$$\begin{pmatrix}
(2,2)&(0,3)\\
(3,0)&(1,1)
\end{pmatrix}$$

If they cooperated (choosing the first strategy) I would double the 6 chocolates and they would have 12 chocolates each. If 1 defected, the defector would have 18 chocolates and the other none. If they both defected they would just have 6 chocolates each.

I asked if they'd like to talk to each other. S, tried but A confidently said: 'no need, I know what you are going to do'. S cooperated and A defected.

There were 1 or 2 'oooos' that were swiftly ended when A proceeded to immediately share his chocolates with A. I in fact ended up just giving the whole box of chocolates I bought:


After this we moved on to talk about best response strategies. 

I asked for a volunteer to player tic-tac-doe with me and we used this as a discussion about best responses:

'Right, now that she has played there, where should I play?'

I put up a picture of +Randall Munroe's tic-tac-toe solution.

All in all it was good fun I think and hopefully helped make the class a bit more 'alive'. I have a (what I think is a) cool idea about a game I'll try and play with my students next week when talking about mixed strategy equilibrium. This could involve a bracket of 16 volunteers...

If you liked the video above, take a look at this one which is pretty awesome too: